Remote estimation of chlorophyll a in optically complex waters based on optical classification

Accurate assessment of phytoplankton chlorophyll a (Chla) concentration in turbid waters by means of remote sensing is challenging due to optically complexity and significant variability of case 2 waters, especially in inland waters with multiple optical types. In this study, a water optical classification algorithm is developed, and two semi-analytical algorithms (three- and four-band algorithm) for estimating Chla are calibrated and validated using four independent datasets collected from Taihu Lake, Chaohu Lake, and Three Gorges Reservoir. The optical classification algorithm is developed using the dataset collected in Taihu Lake from 2006 to 2009. This dataset is also used to calibrate the three- and four-band Chla estimation algorithms. The optical classification technique uses remote sensing reflectance at three bands: Rrs(G), Rrs(650), and Rrs(NIR), where G indicates the location of reflectance peak in the green region (around 560 nm), and NIR is the location of reflectance peak in the near-infrared region (around 700 nm). Optimal reference wavelengths of the three- and four-band algorithm are located through model tuning and accuracy optimization. The three- and four-band algorithm accuracy is further evaluated using other three independent datasets. The improvement of optical classification in Chla estimation is revealed by comparing the performance of the two algorithms for non-classified and classified waters.Using the slopes of the three reflectance bands, the 138 reflectance spectra samples in the calibration dataset are classified into three classes, each with a specific spectral shape character. The three- and four-band algorithm performs well for both non-classified and classified waters in estimating Chla. For non-classified waters, strong relationships are yielded between measured and predicted Chla, but the performance of the two algorithms is not satisfactory in low Chla conditions, especially for samples with Chla below 30 mg m^− 3. For classified waters, the class-specific algorithms perform better than for non-classified waters. Class-specific algorithms reduce considerable mean relative error from algorithms for non-classified waters in Chla predicting. Optical classification makes that there is no need to adjust the optimal position to estimate Chla for other waters using the class-specific algorithms. The findings in this study demonstrate that optical classification can greatly improve the accuracy of Chla estimation in optically complex waters.     

An assessment of chlorophyll-a algorithms available for SeaWiFS in coastal and open areas of the Bay of Bengal and Arabian Sea

Three ocean colour algorithms, OC4v6, Carder and OC5 were tested for retrieving Chlorophyll-a (Chla) in coastal areas of the Bay of Bengal and open ocean areas of the Arabian Sea. Firstly, the algorithms were run using ~ 80 in situ Remote Sensing Reflectance, (R_rs(λ)) data collected from coastal areas during eight cruises from January 2000 to March 2002 and the output was compared to in situ Chla. Secondly, the algorithms were run with ~ 20 SeaWiFS R_rs(λ) and the results were compared with coincident in situ Chla. In both cases, OC5 exhibited the lowest log₁₀-RMS, bias, had a slope close to 1 and this algorithm appears to be the most accurate for both coastal and open ocean areas. Thirdly the error in the algorithms was regressed against Total Suspended Material (TSM) and Coloured Dissolved Organic Material (CDOM) data to assess the co-variance with these parameters. The OC5 error did not co-vary with TSM and CDOM. OC4v6 tended to over-estimate Chla > 2 mg m⁻³ and the error in OC4v6 co-varied with TSM. OC4v6 was more accurate than the Carder algorithm, which over-estimated Chla at concentrations > 1 mg m⁻³ and under-estimated Chla at values < 0.5 mg m⁻³. The error in Carder Chla also co-varied with TSM. The algorithms were inter-compared using > 5500 SeaWiFS R_rs(λ) data from coastal to offshore transects in the Northern Bay of Bengal. There was good agreement between OC4v6 and OC5 in open ocean waters and in coastal areas up to 2 mg m⁻³. There was a strong divergence between Carder and OC5 in open ocean and coastal waters. OC4v6 and Carder tended to over-estimate Chla in coastal areas by a factor of 2 to 3 when TSM > 25 g m⁻³. We strongly recommend the use of OC5 for coastal and open ocean waters of the Bay of Bengal and Arabian Sea. A Chla time series was generated using OC5 from 2000 to 2003, which showed that concentrations at the mouths of the Ganges reach a maxima (~ 5 mg m⁻³) in October and November and were 0.08 mg m⁻³ further offshore increasing to 0.2 mg m⁻³ during December. Similarly in early spring from February to March, Chla was 0.08 to 0.2 mg m⁻³ on the east coast of the Bay.     

Remote chlorophyll-a retrieval in turbid, productive estuaries: Chesapeake Bay case study

Accurate remote assessment of phytoplankton chlorophyll a (chla) concentration is particularly challenging in turbid, productive waters. Recently a conceptual model containing reflectance in three spectral bands in the red and near infra-red range of the spectrum was suggested for retrieving chla concentrations in turbid productive waters; it was calibrated and validated in lakes and reservoirs in Nebraska and Iowa. The objective of this paper is to evaluate the performance of this three band model as well as its special case, the two-band model to estimate chla concentration in Chesapeake Bay, as representative of estuarine Case II waters, and to assess the accuracy of chla retrieval. To evaluate the model performance, dual spectroradiometers were used to measure subsurface spectral radiance reflectance in the visible and near infra-red range of the spectrum. Water samples were collected concurrently and contained widely variable chla (9 to 77.4 mg/m³) and total suspended solids (7-65 mg/L dry wt). Colored dissolved organic matter (CDOM) absorption at 440 nm was 0.20 to 2.50 m^− 1; Secchi disk transparency ranged from 0.28 to 1.5 m. The two- and three-band models were spectrally tuned to select the spectral bands for most accurate chla estimation. Strong linear relationships were established between analytically measured chla and both the three-band model [R^− 1(675)-R^− 1(695)] × R(730) and the two-band model R(720)/R(670), where R(λ) is reflectance at wavelength λ. The three-band model accounted for 81% of variation in chla and allowed estimation of chla with a root mean square error (RMSE) of less than 7.9 mg/m³, whereas the two-band model accounted for 79% of chla variability and RMSE of chla estimation was below 8.4 mg/m³. The three-band model with MERIS spectral bands allows accurate chla estimation with RMSE below 9.1 mg/m³. Two-band model with SeaWiFS bands and MODIS 667 nm and 748 nm bands can estimate chla with RMSE below 11 mg/m³. The findings underlined the rationale behind the conceptual model and demonstrated the robustness of this algorithm for chla retrieval in turbid, productive estuarine waters.     

A simple semi-analytical model for remote estimation of chlorophyll-a in turbid waters: Validation

Accurate assessment of phytoplankton chlorophyll-a (chla) concentrations in turbid waters by means of remote sensing is challenging due to the optical complexity of case 2 waters. We have applied a recently developed model of the form [R_rs^? 1(λ₁) ? R_rs^? 1(λ₂)] × R_rs(λ₃) where R_rs(λ_i) is the remote-sensing reflectance at the wavelength λ_i, for the estimation of chla concentrations in turbid waters. The objectives of this paper are (a) to validate the three-band model as well as its special case, the two-band model R_rs^? 1(λ₁) × R_rs(λ₃), using datasets collected over a considerable range of optical properties, trophic status, and geographical locations in turbid lakes, reservoirs, estuaries, and coastal waters, and (b) to evaluate the extent to which the three-band model could be applied to the Medium Resolution Imaging Spectrometer (MERIS) and two-band model could be applied to the Moderate Resolution Imaging Spectroradiometer (MODIS) to estimate chla in turbid waters.The three-band model was calibrated and validated using three MERIS spectral bands (660–670 nm, 703.75–713.75 nm, and 750?757.5 nm), and the 2-band model was tested using two MODIS spectral bands (λ₁ = 662–672, λ₃ = 743–753 nm). We assessed the accuracy of chla prediction in four independent datasets without re-parameterization (adjustment of the coefficients) after initial calibration elsewhere. Although the validation data set contained widely variable chla (1.2 to 236 mg m^? 3), Secchi disk depth (0.18 to 4.1 m), and turbidity (1.3 to 78 NTU), chla predicted by the three-band algorithm was strongly correlated with observed chla (r² > 0.96), with a precision of 32% and average bias across data sets of ? 4.9% to 11%. Chla predicted by the two-band algorithm was also closely correlated with observed chla (r² > 0.92); however, the precision declined to 57%, and average bias across the data sets was 18% to 50.3%. These findings imply that, provided that an atmospheric correction scheme for the red and NIR bands is available, the extensive database of MERIS and MODIS imagery could be used for quantitative monitoring of chla in turbid waters.     

New models for retrieving and partitioning the colored dissolved organic matter in the global ocean: Implications for remote sensing

Despite the importance of CDOM to upper ocean biogeochemical processes and optics, our current understanding of its spatial and temporal distributions and the factors controlling these distributions is very limited. This eventually prevents an understanding of its relationship to the pool of dissolved organic carbon in coastal and open oceans. This work aims to present a new approach for accurate modeling of absorption spectra of CDOM (a_cdom) and deriving information on its composition in global ocean waters. The modeling approach uses measurements (in situ) of the remote sensing reflectances at two wavelengths (denoted ₄₄₃⁵⁵⁵R_rs) to estimate a_cdom(350) and a_cdom(412), applies them to determine two spectral slopes of an exponential curve fit (S) and a hyperbolic curve fit (γ), derives an appropriate parameter (γ^o) for grading the CDOM compositional changes from a_cdom (350) and γ, and finally employs a_cdom(350), S, and γ^o in a modified exponential model to describe a_cdom(λ) as a function of wavelength. The robustness of this model was rigorously tested on three independent datasets, such as NOMAD in situ data, NOMAD SeaWiFS match-ups data and IOCCG simulated data (all of them contain a_cdom(λ) and R_rs(λ)), which represent a variety of waters within coastal and offshore regions around the world. Accuracy of the retrievals found with the new models was generally excellent, with MRE (mean relative error) and RMSE (root mean square error) of − 5.64-3.55% and 0.203-0.318 for the NOMAD in situ datasets, and − 5.63 to −0.98% and 0.136-0.241 for the NOMAD satellite datasets respectively (for λ₄₁₂ to λ₆₇₀). When used with SeaWiFS images collected over the regional and global waters, the new model showed the highest surface abundances of CDOM within the subpolar gyres and continental shelves dominated by terrestrial inputs (and perhaps local production) of colored dissolved materials, and the lowest surface abundances of CDOM in the central subtropical gyres and the open oceans presumably regulated by photobleaching phenomenon, bacterial activity and local processes. Significant interseasonal and interannual seasonal changes in the terrestrially-derived CDOM distributions were noticed from these new products that closely corresponded with the global mean runoff/river discharge induced by climate change/warming scenarios.     

Assessing the potential of SeaWiFS and MODIS for estimating chlorophyll concentration in turbid productive waters using red and near-infrared bands

Bio-optical algorithms for remote estimation of chlorophyll-a concentration (Chl) in case-1 waters exploit the upwelling radiation in the blue and green spectral regions. In turbid productive waters other constituents, that vary independently of Chl, absorb and scatter light in these spectral regions. As a consequence, the accurate estimation of Chl in turbid productive waters has so far not been feasible from satellite sensors. The main purpose of this study was to evaluate the extent to which near-infrared (NIR) to red reflectance ratios could be applied to the Sea Wide Field-of-View Sensor (SeaWiFS) and the Moderate Imaging Spectrometer (MODIS) to estimate Chl in productive turbid waters. To achieve this objective, remote-sensing reflectance spectra and relevant water constituents were collected in 251 stations over lakes and reservoirs with a wide variability in optical parameters (i.e. 4 ≤ Chl ≤ 240 mg m^− 3; 18 ≤ Secchi disk depth ≤ 308 cm). SeaWiFS and MODIS NIR and red reflectances were simulated by using the in-situ hyperspectral data. The proposed algorithms predicted Chl with a relative random uncertainty of approximately 28% (average bias between − 1% and − 4%). The effects of reflectance uncertainties on the predicted Chl were also analyzed. It was found that, for realistic ranges of R_rs uncertainties, Chl could be estimated with a precision better than 40% and an accuracy better than ± 35%. These findings imply that, provided that an atmospheric correction scheme specific for the red-NIR spectral region is available, the extensive database of SeaWiFS and MODIS images could be used to quantitatively monitor Chl in turbid productive waters.     

Estimating phytoplankton biomass in coastal waters of Alaska using airborne remote sensing

Empirical airborne remote-sensing relationships were examined to estimate chlorophyll a concentration in the first optical depth (chl_FOD) of coastal waters of Afgonak/Kodiak Islands during July-August 2002. Band-ratio and spectral-curvature models were tested using satellite remote-sensing reflectance (R_rs(λ)) measurements. Additional shipboard and airborne R_rs(λ) data were also analysed to evaluate consistency of proposed chl_FOD-R_rs(λ) relationships. Validation of chlorophyll algorithms was performed using data collected in the northern-part of the Gulf of Alaska and Bering Sea during 1996, 2002, and 2003 cruises. Likewise, oceanographic conditions during the surveys were typified to interpret variability of chl_FOD fields. The SeaWiFS band-ratio algorithm OC2d was the most sensitive R_rs combination (R_rs(509)/R_rs(553)) to detect chl_FOD variability. Conversely, OC2a (R_rs(412)/R_rs(553)) had the lowest performance to derive chl_FOD values. No valid statistical regressions were established for spectral-curvature relationships in the blue spectrum (< 500 nm). Fertile waters (> 5 mg m^− 3) were preferentially located over shallow banks (∼50 m) and at the entrance of the bays. The approach used in this study to derive chl_FOD values could be universal for Alaskan coastal waters. However, chl_FOD-R_rs(λ) relationships must be calibrated locally for a given season.     

Relationships between suspended mineral concentrations and red-waveband reflectances in moderately turbid shelf seas

This paper considers the uncertainties that arise in estimating the concentration of suspended minerals by optical remote sensing in waters which contain unknown concentrations of other optically significant constituents. Relationships between suspended mineral concentrations and remote sensing reflectance were calculated by radiative transfer modelling using representative specific inherent optical properties (SIOPs) for phytoplankton (CHL), suspended mineral particles of terrigenous origin (MSS_ter) and coloured dissolved organic matter (CDOM) that were derived from measurements at 173 stations in UK shelf seas. When only suspended minerals were present, remote sensing reflectance (R_rs) was related to MSS_ter by a family of saturation curves whose shape depended strongly on wavelength. However the addition of CHL and CDOM made this relationship considerably more complex. Polynomial expressions were therefore derived for the maximum and minimum values of MMS_ter consistent with a given R_rs667 in the presence of independently varying concentrations of CHL and CDOM. For CHL ranging from 0 to 10 mg m⁻³ and CDOM from 0 to 1 m⁻¹, for example, an R_rs667 observation 0.01 sr⁻¹ could corresponded to MSS_ter values between 7 and 12 g m⁻³. The presence of biogenic minerals in the form of diatom frustules, MSS_dia had little influence on the accuracy of MSS_ter retrieval. The degree of variability in the relationship between MSS_ter and Rrs667 predicted by the model was confirmed by measurements of radiometric profiles and mineral concentrations at 110 Irish Sea stations. Uncertainties in the remote sensing of MSS_ter in coastal waters are more appropriately indicated by upper and lower limits set according to the likely ranges of other optically significant constituents than by percentage errors. Moreover, the influence of these constituents should be eliminated before variations in the relationship between MSS_ter and Rrs are attributed to qualitative changes in mineral particle characteristics.     

Validation of MERIS ocean-color products in the Bohai Sea: A case study for turbid coastal waters

An extensive in situ data set in the Bohai Sea of China was collected to assess radiometric properties and concentrations of ocean constituents derived from Medium Resolution Imaging Spectrometer (MERIS). The data collected include spectral normalized water-leaving radiance L_wn(λ) and concentrations of suspended particulate matter (SPM) and chlorophyll a (Chl-a). A strict spatio-temporal match-up method was adopted in view of the complexity and variability of the turbid coastal area, resulting in 13, 48 and 18 match-ups for MERIS L_wn(λ), SPM and Chl-a estimates, respectively. For MERIS L_wn(λ), the match-ups showed mean absolute percentage differences (APD) of 17%-20% in the 412, 443, 620 and 665 nm bands, whereas L_wn(λ) at bands from 490 and 560 nm had better APD of 15-16%. The band ratio of L_wn(490) to L_wn(560) of the satellite data was in good agreement with in situ observations with an APD of 4%. MERIS SPM and Chl-a products overestimated the in situ values, with the APD of approximately 50% and 60%, respectively. When match-up criteria were relaxed, the assessment results degraded systematically. Hence, in turbid coastal areas where temporal variability and spatial heterogeneity of bio-optical properties may be pronounced as the result of terrestrial influences and local dynamics, the strict spatio-temporal match-up is recommended.     

Remote estimation of chl-a concentration in turbid productive waters — Return to a simple two-band NIR-red model?

Today the water quality of many inland and coastal waters is compromised by cultural eutrophication in consequence of increased human agricultural and industrial activities. Remote sensing is widely applied to monitor the trophic state of these waters. This study investigates the performance of near infrared-red models for the remote estimation of chlorophyll-a concentrations in turbid productive waters and evaluates several near infrared-red models developed within the last 34 years. Three models were calibrated for a dataset with chlorophyll-a concentrations from 0 to 100 mg m⁻³ and validated for independent and statistically different datasets with chlorophyll-a concentrations from 0 to 100 mg m⁻³ and 0 to 25 mg m⁻³ for the spectral bands of the MEdium Resolution Imaging Spectrometer (MERIS) and MODerate resolution Imaging Spectroradiometer (MODIS). The MERIS two-band model estimated chlorophyll-a concentrations slightly more accurately than the more complex models, with mean absolute errors of 2.3 mg m⁻³ for chlorophyll-a concentrations from 0 to 100 mg m⁻³ and 1.2 mg m⁻³ for chlorophyll-a concentrations from 0 to 25 mg m⁻³. Comparable results from several near infrared-red models with different levels of complexity, calibrated for inland and coastal waters around the world, indicate a high potential for the development of a simple universally applicable near infrared-red algorithm.     

Estimation of monthly air-sea CO2 flux in the southern Atlantic and Indian Ocean using in-situ and remotely sensed data

Empirical relationships between the sea surface partial pressure of carbon dioxide (pCO₂), sea surface chlorophyll-a concentration (Chl-a), and sea surface temperature (SST), were derived from shipboard pCO₂ measurements in sea water and atmosphere, in-situ Chl-a, and SST data along cruise tracks between Zhongshan Station in East Antarctica and Changcheng Station on the Antarctic Peninsula in December 1999, January 2000, December 2004 and January 2005 during the CHINARE XVI and XXI campaigns. These relationships were then applied to datasets of remotely sensed Chl-a and SST to estimate the monthly air-sea carbon flux and the uptake of atmospheric CO₂ in the southern Atlantic and Indian Ocean. The results show significant spatial and temporal variability of carbon flux in the southern Atlantic and Indian Ocean. The monthly uptakes of atmospheric CO₂ in the region from 50°S to the ice edge between 60°W and 80°E are − 0.00355 GtC, − 0.00573 GtC in December 1999 and January 2000, and − 0.00361 GtC, − 0.00525 GtC in December 2004 and January 2005, respectively.     

Embedding meshes into locally twisted cubes

As a newly introduced interconnection network for parallel computing, the locally twisted cube possesses many desirable properties. In this paper, mesh embeddings in locally twisted cubes are studied. Let LTQ_n(V, E) denote the n-dimensional locally twisted cube. We present three major results in this paper: (1) For any integer n ? 1, a 2 × 2ⁿ⁻¹ mesh can be embedded in LTQ_n with dilation 1 and expansion 1. (2) For any integer n ? 4, two node-disjoint 4 × 2ⁿ⁻³ meshes can be embedded in LTQ_n with dilation 1 and expansion 2. (3) For any integer n ? 3, a 4  × (2ⁿ⁻² − 1) mesh can be embedded in LTQ_n with dilation 2. The first two results are optimal in the sense that the dilations of all embeddings are 1. The embedding of the 2 × 2ⁿ⁻¹ mesh is also optimal in terms of expansion. We also present the analysis of 2p × 2q mesh embedding in locally twisted cubes.     

Fast, prime factor, discrete Fourier transform algorithms over GF(2) for 8 ? m ? 10

In this paper it is shown that Winograd’s algorithm for computing convolutions and a fast, prime factor, discrete Fourier transform (DFT) algorithm can be modified to compute Fourier-like transforms of long sequences of 2^m − 1 points over GF(2^m), for 8 ? m ? 10. These new transform techniques can be used to decode Reed-Solomon (RS) codes of block length 2^m − 1. The complexity of this new transform algorithm is reduced substantially from more conventional methods. A computer simulation verifies these new results.     

Remote sensing of water clarity in Tampa Bay

We examined the spatial and temporal variability of the Secchi Disk Depth (SDD) within Tampa Bay, Florida, using the Sea-viewing Wide Field-of-View Sensor (SeaWiFS) satellite imagery collected from September 1997 to December 2005. SDD was computed using a two-step process, first estimating the diffuse light attenuation coefficient at 490 nm, K_d(490), using a semi-analytical algorithm and then SDD using an empirical relationship with K_d(490). The empirical SDD algorithm (SDD = 1.04 × K_d(490)^− 0.82, 0.9 < SDD < 8.0 m, r² = 0.67, n = 80) is based on historical SDD observations collected by the Environmental Protection Commission of Hillsborough County (EPCHC) in Tampa Bay. SeaWiFS derived SDD showed distinctive seasonal variability, attributed primarily to chlorophyll concentrations and color in the rainy season and to turbidity in the dry season, which are in turn controlled by river runoff and winds or wind-induced sediment resuspension, respectively. The Bay also experienced strong interannual variability, mainly related to river runoff variability. As compared to in situ single measurements, the SeaWiFS data provide improved estimates of the “mean” water clarity conditions in this estuary because of the robust, frequent, and synoptic coverage. Therefore we recommend incorporation of this technique for routine monitoring of water quality in coastal and large estuarine waters like Tampa Bay.     

Estimation of chlorophyll-a concentration in coastal waters with HJ-1A HSI data using a three-band bio-optical model and validation

Accurate assessment of phytoplankton chlorophyll-a (chl-a) concentration in turbid waters by means of remote sensing is challenging because of the optical complexity of case 2 waters. We applied a bio-optical model of the form [R^–1(λ₁) – R^–1(λ₂)](λ₃), where R(λ_i) is the remote-sensing reflectance at wavelength λ_i, to estimate chl-a concentration in coastal waters. The objectives of this article are (1) to validate the three-band bio-optical model using a data set collected in coastal waters, (2) to evaluate the extent to which the three-band bio-optical model could be applied to the spectral radiometer (SR) ISI921VF-512T data and the hyperspectral imager (HSI) data on board the Chinese HJ-1A satellite, (3) to evaluate the application prospects of HJ-1A HSI data in case 2 waters chl-a concentration mapping. The three-band model was calibrated using three SR spectral bands (λ₁ = 664.9 nm, λ₂ = 706.54 nm, and λ₃ = 737.33 nm) and three HJ-1A HSI spectral bands (λ₁ = 637.725 nm, λ₂ = 711.495 nm, and λ₃ = 753.750 nm). We assessed the accuracy of chl-a prediction with 21 in situ sample plots. Chl-a predicted by SR data was strongly correlated with observed chl-a (R² = 0.93, root mean square error (RMSE) = 0.48 mg m^–3, coefficient of variation (CV) (RMSE/mean(chl-a_mea)) = 3.72%). Chl-a predicted by HJ-1A HSI data was also closely correlated with observed chl-a (R² = 0.78, RMSE = 0.45 mg m^–3, CV (RMSE/mean(chl-a_mea)) = 7.51%). These findings demonstrate that the HJ-1A HSI data are promising for quantitative monitoring of chl-a in coastal case-2 waters.     

An assessment of the black ocean pixel assumption for MODIS SWIR bands

Recent studies show that an atmospheric correction algorithm using shortwave infrared (SWIR) bands improves satellite-derived ocean color products in turbid coastal waters. In this paper, the black pixel assumption (i.e., zero water-leaving radiance contribution) over the ocean for the Moderate Resolution Imaging Spectroradiometer (MODIS) SWIR bands at 1240, 1640, and 2130 nm is assessed for various coastal ocean regions. The black pixel assumption is found to be generally valid with the MODIS SWIR bands at 1640 and 2130 nm even for extremely turbid waters. For the MODIS 1240 nm band, however, ocean radiance contribution is generally negligible in mildly turbid waters such as regions along the U.S. east coast, while some slight radiance contributions are observed in extremely turbid waters, e.g., some regions along the China east coast, the estuary of the La Plata River. Particularly, in the Hangzhou Bay, the ocean radiance contribution at the SWIR band 1240 nm results in an overcorrection of atmospheric and surface effects, leading to errors of MODIS-derived normalized water-leaving radiance at the blue reaching ~ 0.5 mW cm^− 2 μm^− 1 sr^− 1. In addition, we found that, for non-extremely turbid waters, i.e., the ocean contribution at the near-infrared (NIR) band < ~ 1.0 mW cm^− 2 μm^− 1 sr^− 1, there exists a good relationship in the regional normalized water-leaving radiances between the red and the NIR bands. Thus, for non-extremely turbid waters, such a red-NIR radiance relationship derived regionally can possibly be used for making corrections for the regional NIR ocean contributions without using the SWIR bands, e.g., for atmospheric correction of ocean color products derived from the Sea-viewing Wide Field-of-view Sensor (SeaWiFS).     

Load-sharing system model and its application to the real data set

This study deals with the classical and Bayesian estimation of the parameters of a k-components load-sharing parallel system model in which each component's lifetime follows Lindley distribution. Initially, the failure rate of each of the k components in the system is h(t,θ₁) until the first component failure. However, upon the first failure within the system, the failure rates of the remaining (k − 1) surviving components change to h(t,θ₂) and remain the same until next failure. After second failure, the failure rates of (k − 2) surviving components change to h(t,θ₃) and finally when the (k − 1)th component fails, the failure rate of the last surviving component becomes h(t,θ_k). In classical set up, the maximum likelihood estimates of the load share parameters, system reliability and hazard rate functions along with their standard errors are computed. 100 × (1 − γ)% confidence intervals and two bootstrap confidence intervals for the parameters have also been constructed. Further, by assuming Jeffrey's invariant and gamma priors of the unknown parameters, Bayes estimates along with their posterior standard errors and highest posterior density credible intervals of the parameters are obtained. Markov Chain Monte Carlo technique such as Metropolis–Hastings algorithm has been utilized to generate draws from the posterior densities of the parameters.     

Estimating chlorophyll a concentrations from remote-sensing reflectance in optically shallow waters

A multi-spectral classification and quantification technique is developed for estimating chlorophyll a concentrations, Chl, in shallow oceanic waters where light reflected by the bottom can contribute significantly to the above-water remote-sensing reflectance spectra, R_rs(λ). Classification criteria for determining bottom reflectance contributions for shipboard R_rs(λ) data from the west Florida shelf and Bahamian waters (1998-2001; n = 451) were established using the relationship between R_rs(412)/R_rs(670) and the spectral curvature about 555 nm, [R_rs(412) ? R_rs(670)]/R_rs(555)². Chlorophyll concentrations for data classified as “optically deep” and “optically shallow” were derived separately using best-fit cubic polynomial functions developed from the band-ratios R_rs(490)/R_rs(555) and R_rs(412)/R_rs(670), respectively. Concentrations for transitional data were calculated from weighted averages of the two derived values. The root-mean-square error (RMSE_log10) calculated for the entire data set using the new technique was 14% lower than the lowest error derived using the best individual band-ratio. The standard blue-to-green, band-ratio algorithm yields a 26% higher RMSE_log10 than that calculated using the new method. This study demonstrates the potential of quantifying chlorophyll a concentrations more accurately from multi-spectral satellite ocean color data in oceanic regions containing optically shallow waters.     

Multi-sensor model-data fusion for estimation of hydrologic and energy flux parameters

Model-data fusion offers considerable promise in remote sensing for improved state and parameter estimation particularly when applied to multi-sensor image products. This paper demonstrates the application of a ‘multiple constraints’ model-data fusion (MCMDF) scheme to integrating AMSR-E soil moisture content (SMC) and MODIS land surface temperature (LST) data products with a coupled biophysical model of surface moisture and energy budgets for savannas of northern Australia. The focus in this paper is on the methods, difficulties and error sources encountered in developing an MCMDF scheme and enhancements for future schemes. An important aspect of the MCMDF approach emphasized here is the identification of inconsistencies between model and data, and among data sets.The MCMDF scheme was able to identify that an inconsistency existed between AMSR-E SMC and LST data when combined with the coupled SEB-MRT model. For the example presented, an optimal fit to both remote sensing data sets together resulted in an 84% increase in predicted SMC and 0.06% increase for LST relative to the fit to each data set separately. That is the model predicted on average cooler LST's (∼ 1.7 K) and wetter SMC values (∼ 0.04 g cm^− 3) than the satellite image products. In this instance we found that the AMSR-E SMC data on their own were poor constraints on the model. Incorporating LST data via the MCMDF scheme ameliorated deficiencies in the SMC data and resulted in enhanced characterization of the land surface soil moisture and energy balance based on comparison with the MODIS evapotranspiration (ET) product of Mu et al. [Mu, Q., Heinsch, F.A, Zhao, M. and Running, S.W. (in press), Development of a global evapotranspiration algorithm based on MODIS and global meteorology data, Remote Sensing of Environment.]. Canopy conductance, g_C, and latent heat flux, λE, from the MODIS ET product were in good agreement with RMSEs for g_C = 0.5 mm s^− 1 and for λE = 18 W m^− 2, respectively. Differences were attributable to a greater canopy-to-air vapor pressure gradient in the MCMDF approach obtained from a more realistic partitioning of soil surface and canopy temperatures.